recent advances in dynamic facility layout research
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University of Calgary
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Haskayne School of Business Haskayne School of Business Research & Publications
2017-09-08
Recent advances in dynamic facility layout research
Zhu, Tianyuan; Balakrishnan, Jaydeep; Cheng, Chun-Hung
INFOR: Information Systems and Operational Research
Zhu, T., Balakrishnan, J., & Cheng, C.-H. (2017). Recent advances in dynamics facility layout
research. "Information Systems and Operational Research".
https://doi.org/10.1080/03155986.2017.1363591
http://hdl.handle.net/1880/108918
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Recent advances in dynamic facility layout research
Tianyuan Zhua*, Jaydeep Balakrishnana and Chun Hung Chengb
aHaskayne School of Business, University of Calgary, Calgary, Canada;
bDepartment of Systems Engineering and Engineering Management, The Chinese
University of Hong Kong, Hong Kong, China
Scurfield Hall, 2500 University Dr. NW, Calgary, Alberta, Canada T2N 1N4,
Accepted for publication in INFOR- Information Systems and Operational Research,
August 2017.
Recent advances in dynamic facility layout research
Abstract
It has been nearly two decades since Balakrishnan and Cheng (1998) reviewed the
literature in dynamic facility layout. In these intervening years, many advances have
been made in modelling as well as in the solution methods. In this study, models and
solutions that address the dynamic facility layout problem (DFLP) are examined and
categorized. Our review finds that, the recent DFLP models consider more complex
design features and constraints. Further, only a few DFLP studies have adopted exact
methods, while most of the effective algorithms used are heuristics, metaheuristics and
hybrid approaches. Future research directions are also identified.
Keywords: dynamic facility layout; modelling; algorithms; metaheuristics;
survey
1 Introduction
This paper reviews recent work in the dynamic facility layout problem (DFLP, also
called the dynamic plant layout problem – DPLP) where the facility may be redesigned
during the planning horizon due to material flow changes. The DFLP is a relatively new
research area compared to the static plant layout problem (SPLP). For a detailed
analysis of the early work in DFLP, the reader may refer to Balakrishnan and Cheng
(1998).
In the two decades since Balakrishnan and Cheng’s (1998) review, significant
progress has been made in the complexity of the models as well as in the solution
methods. Thus, we feel that it is appropriate to provide an analysis of recent
developments, which will give researchers a good understanding of the state-of-the-art
in DFLP research. The remainder of the paper is organized as follows. The next section
explains the models used by researchers. Section 3 discusses the solution methods
applied. Finally, Section 4 summarizes the paper and suggests possible future research
directions.
2 Dynamic facility layout modelling
Drira et al. (2007) summarized essential features to characterize facility layout problems
(FLP). Based on Drira et al’s (2007) framework, the DFLP can be studied from the
following aspects: problem formulations including objectives and constraints, and
facility characteristics such as the specificities of the manufacturing systems, the facility
shapes, and the layout configurations.
2.1 Problem formulations
In the past twenty years, different kinds of mathematical models have been used to
formulate DFLP, which include the modified quadratic assignment problem (QAP),
mixed integer programming (MIP), graph theoretic models (GT) and so on.
More than half of the DFLP studies are modelled with discrete representation by
modified QAP. Generally, in DFLPs formulated by modified QAP, the planar region is
divided into a number of rectangular sub-regions with the same size and shape. Each
sub-region is assigned to one department, so as to minimize the sum of the material
handling cost and rearrangement cost. A typical formulation is shown as follows
(Balakrishnan et al. 2003):
min ∑ ∑ ∑ ∑ ∑ 𝑓𝑡𝑖𝑘
𝑛
𝑙=1
𝑑𝑡𝑗𝑙𝑋𝑡𝑖𝑗𝑋𝑡𝑘𝑙
𝑛
𝑘=1
𝑛
𝑗=1
𝑛
𝑖=1
𝑃
𝑡=1
+ ∑ ∑ ∑ ∑ ∑ 𝐴𝑡𝑖𝑗𝑙
𝑛
𝑙=1
𝑌𝑡𝑖𝑗𝑙
𝑛
𝑘=1
𝑛
𝑗=1
𝑛
𝑖=1
𝑃
𝑡=2
(1)
Subject to
∑ 𝑋𝑡𝑖𝑗
𝑁
𝑖=1
= 1; 𝑗 = 1, 2, … , 𝑛; 𝑡 = 1, 2, … 𝑃 (2)
∑ 𝑋𝑡𝑖𝑗
𝑁
𝑗=1
= 1; 𝑖 = 1, 2, … , 𝑛; 𝑡 = 1, 2, … 𝑃 (3)
𝑌𝑡𝑖𝑗𝑙 = 𝑋(𝑡−1)𝑖𝑗 𝑋𝑡𝑖𝑙; 𝑖, 𝑗, 𝑙 = 1, 2, … , 𝑛; 𝑡 = 2, … 𝑃 (4)
where 𝑓𝑡𝑖𝑘 is the flow cost from department 𝑖 to department 𝑘 in period 𝑡; 𝑑𝑡𝑗𝑙 is the
distance from location 𝑗 to department 𝑙 in period 𝑡; 𝑋𝑡𝑖𝑗 is a 0-1 variable for locating
department 𝑖 at location 𝑗 in period 𝑡; 𝐴𝑡𝑖𝑗𝑚 is fixed cost of shifting department 𝑖 from 𝑗
to 𝑚 in period 𝑡 (𝐴𝑡𝑖𝑗𝑗 = 0); and 𝑌𝑡𝑖𝑗𝑚 is a 0-1 variable for shifting department 𝑖 from 𝑗
to 𝑚 in period 𝑡. The objective in (1) is to minimize the sum of the material handling
cost (first term) and the layout rearrangement cost (second term). Eq. (2) ensures every
department to be assigned. Eq. (3) requires every location having a department assigned
to it. Eq. (4) assigns 𝑌𝑡𝑖𝑗𝑚 a value of 1 only when a department has been shifted in the
period.
Considering departments with unequal sizes, Kochhar and Heragu (1999)
assumed that the facility is divided into a grid of squares of unit area and each
department is assigned to one or more unit squares based on its area requirements (see
Figure 1). Samarghandi et al. (2013) also considered unequal area and formulated a
multi-objective DFLP using modified QAP. Different from Kochhar and Heragu
(1999), they assumed that a department can only be placed in certain locations in each
period. The formulation is shown as follows (Samarghandi et al. 2013):
min𝑧1 = ∑ ∑ ∑ ∑ ∑ 𝑐𝑖𝑚𝑡
𝑁
𝑛=1
∙ 𝑑𝑗𝑛 ∙ 𝜋𝑖𝑚𝑡 ∙ 𝑋𝑖𝑗𝑡 ∙ 𝑋𝑚𝑛𝑡
𝑁
𝑚=1
𝑁
𝑗=1
𝑁
𝑖=1
𝑇
𝑡=1
+ ∑ ∑ ∑ ∑ 𝑠𝑖 ∙
𝑁
𝑙=1
𝑌𝑖𝑗𝑙𝑡
𝑁
𝑗=1
𝑁
𝑖=1
𝑇
𝑡=2
(5)
max𝑧2 = ∑ ∑ ∑ ∑ ∑(𝑤𝑖𝑗𝑡 ∙ 𝑉𝑖𝑎𝑏𝑡 ∙ 𝑉𝑗𝑎(𝑏+1)𝑡)
𝑁
𝑗=1
𝑁
𝑖=1
𝐵
𝑏=1
𝐴−1
𝑎=1
𝑇
𝑡=1
+ ∑ ∑ ∑ ∑ ∑(𝑤𝑖𝑗𝑡 ∙ 𝑉𝑖𝑎𝑏𝑡 ∙ 𝑉𝑗(𝑎+1)𝑏𝑡)
𝑁
𝑗=1
𝑁
𝑖=1
𝐵−1
𝑏=1
𝐴
𝑎=1
𝑇
𝑡=1
(6)
Subject to
∑ 𝑋𝑖𝑗𝑡
𝑁
𝑖=1
= 1; 𝑗 = 1, 2, … , 𝑁; 𝑡 = 1, 2, … 𝑇 (7)
∑ 𝑋𝑖𝑗𝑡
𝑁
𝑗∈𝑄𝑖𝑡
= 1; 𝑖 = 1, 2, … , 𝑁; 𝑡 = 1, 2, … 𝑇 (8)
𝑌𝑖𝑗𝑙𝑡 = 𝑋𝑖𝑗(𝑡−1) ∙ 𝑋𝑖𝑙𝑡; 1 ≤ 𝑖, 𝑗, 𝑙 ≤ 𝑁; 2 ≤ 𝑡 ≤ 𝑇 (9)
𝑉𝑖𝑎𝑏𝑡 = 𝑋𝑖((𝑎−1)𝐴+𝑏)𝑡; 𝑖 = 1, 2, … , 𝑁; (10)
𝑎 = 1, 2, … , 𝐴; 𝑏 = 1, 2, … , 𝐵; 𝑡 = 1, 2, … , 𝑇
𝑋𝑖𝑗𝑡 = {1 if facility i is assigned to location j in period t0 otherwise
(11)
The two objectives involved are minimizing total transportation and shifting
costs (Eq. (5)) and maximizing closeness rating value (Eq. (6)). In Eq. (5), 𝑐𝑖𝑗𝑡 is the
cost of handling one unit of product from facility 𝑖 to facility 𝑗 in period 𝑡 (1 ≤ 𝑡 ≤ 𝑇).
𝑑𝑖𝑗 (1 ≤ 𝑖, 𝑗 ≤ 𝑁) is the distance between location 𝑖 and 𝑗. 𝜋𝑖𝑗𝑡 (1 ≤ 𝑡 ≤ 𝑇, 1 ≤ 𝑖, 𝑗 ≤
𝑁 ) is the amount of transportation between facility 𝑖 and facility 𝑗 in period 𝑡.
𝑆𝑖 (1 ≤ 𝑖 ≤ 𝑁) is the shifting cost when facility 𝑖 is shifted from a location to another
passing through periods. In Eq. (6), 𝑤𝑖𝑗𝑡 (1 ≤ 𝑖, 𝑗 ≤ 𝑁, 1 ≤ 𝑡 ≤ 𝑇) is the closeness
rating value of facilities 𝑖 and 𝑗 in period 𝑡. In Eq. (8), 𝑄𝑖𝑡 (1 ≤ 𝑖 ≤ 𝑁, 1 ≤ 𝑡 ≤ 𝑇 ) is
the set of locations where facility 𝑖 can be placed in period 𝑡.
Chan and Malmborg (2010) developed a model for dynamic line layout problem
considering unequal size work centres, multiple types of material handling devices and
stochastic demand. In this model, as the material handling cost is piecewise linear, the
robust solutions are obtained by solving an enumeration of the QAP instead of a single
QAP. Azevedo et al. (2017) examined reconfigurable multi-facility layout problem
considering the location of departments within a group of facilities, and the location of
departments inside each facility itself. This dynamic multi-facility layout problem was
formulated based on QAP with multiple objectives and unequal areas. In addition to
minimizing material handling and rearrangement costs, Pourvaziri and Pierreval (2017)
also considered the amount of work-in-process in a dynamic facility layout system.
Hence, in their research, the DFLP is formulated by a mathematical model combining a
developed QAP and an open queuing network.
Figure 1 Examples of layouts for one floor in a multi-floor FLP. (Kochhar and Heragu
1999)
Some DFLPs are also formulated with discrete representation considering equal
area facilities but through MIP, as the problems they intend to solve are more
complicated. These studies often combine DFLP with other system problems or
important manufacturing attributes. For instance, Kia et al. (2012) proposed a novel
MIP model for the layout design of a dynamic cellular manufacturing system which
covers a number of important manufacturing and design features including intra-cell
layout, inter-cell layout, multi-rows layout of equal area facilities, alternate process
routings, operation sequence, processing time, production volume of parts, purchasing
machine, duplicate machines, machine capacity, lot splitting and flexible
reconfiguration.
Instead of discrete representation, a number of DFLP studies are formulated
with continuous representations by MIP for unequal size facilities, in which the
dimensions of facilities do not take integer values and the facilities can be located
anywhere on the shop floor (Moslemipour et al. 2012). In these studies, facilities in the
plant site are often located by their centroid coordinates. Such DFLP formulations are
also suitable for designing a detailed layout where the location of pick-up/drop-off
points can also be determined. For example, Jolai et al. (2012) considered a multi-
objective DFLP with unequal fixed size departments and pick-up/drop-off locations,
and modelled the problem using MIP. In their model, (𝑥𝑡𝑖, 𝑦𝑡𝑖) is the centroid
coordinate of department 𝑖 in period 𝑡. 𝑥𝑡𝑖𝑗′ and 𝑦𝑡𝑖𝑗
′ are horizontal and vertical
distances between centroid of department 𝑖 and department 𝑗 in period 𝑡. The distance
between two facilities in period 𝑡 is then expressed by the following Eq. (12) (Jolai et al.
2012):
𝑑𝑡𝑖𝑗 = 𝑥𝑡𝑖𝑗′ + 𝑦𝑡𝑖𝑗
′ = |𝑥𝑡𝑖 − 𝑥𝑡𝑗| + |𝑦𝑡𝑖 − 𝑦𝑡𝑗| (12)
One of the four objectives considered by Jolai et al. (2012) is to minimize the total
material handling cost (Eq. (13)):
Minimze: ∑ ∑ ∑ 𝐶𝑡𝑖𝑗[(𝑥𝑡𝑖𝑗′ + 𝑦𝑡𝑖𝑗
′ )
𝑁
𝑗=1
𝑁
𝑖=1
𝑇
𝑡=1
+ (sgn𝑡𝑖 ∗ 𝑑𝑝𝑡𝑖 + sgn𝑡𝑗 ∗ 𝑑𝑝𝑡𝑗)]
(13)
In Eq. (13), 𝐶𝑡𝑖𝑗 is the cost of material handling (a unit distance) between
department 𝑖 and department 𝑗 in period 𝑡. The calculation of total material handling
cost considers both the distance between two departments 𝑖 and 𝑗 and the distance
between the department centroid and its pick-up/drop-off location. 𝑑𝑝𝑡𝑖 represents the
distance between the centroid and the pick-up/drop-off location of department 𝑖, which
depends on 𝑜𝑡𝑖 (orientation of department 𝑖; 0: vertical, 1: horizontal), 𝑝𝑡𝑖′ and 𝑝𝑡𝑖
′′ (Eq.
(14) - (15)), and sgn𝑡𝑖 is a sign variable which indicates the whether the relative
location of departments 𝑖 and 𝑗 is positive or negative. DFLPs modelled by MIP are
summarized in Table 1.
𝑝𝑡𝑖′ = {
1 if pick − up drop − off⁄ point is in longer edge of department 𝑖 in period 𝑡
0 otherwise
(14)
𝑝𝑡𝑖′′ = {
1 if pick − up drop − off⁄ point is in north − west edges of department 𝑖 in period 𝑡
0 if pick − up drop − off⁄ point is in south − east edges of department 𝑖 in period 𝑡
(15)
Table 1 DFLPs formulated by MIP.
Problem formulation Authors
MIP with equal areas
Krishnan et al. (2006), Bashiri and Dehghan (2010), Kia et al.
(2012), Kia et al. (2013), Kia et al. (2014), Shafigh et al.
(2015), Shafigh et al. (2017)
MIP with unequal
areas
Yang and Peters (1998), Corry and Kozan (2004), Dunker et
al. (2005), McKendall Jr and Hakobyan (2010), Jolai et al.
(2012), Abedzadeh et al. (2013), Mazinani et al. (2013),
Derakhshan Asl and Wong (2015), Kia et al. (2015), Kulturel-
Konak and Konak (2015), Li et al. (2015), Wang et al. (2015),
Xu and Song (2015)
DFLP can also be modelled as a graph, which consists of a number of vertices
(nodes) and edges. The vertices (nodes) in the graph represent the facilities. The
adjacency of each pair of facilities is represented using the edge weight, which is known
in advance (Foulds and Robinson 1978). The edge weights can also be used to indicate
the benefit or the cost of two adjacent facilities. When the edge weights represent the
benefits, the objective considered in the DFLP is to arrange the facilities so as to
maximize the total benefits. Dong et al. (2009) and Erel et al. (2003) formulated the
DFLP with GT models.
In regard to the data used in the DFLP formulations, given the uncertainties in
the problem, some studies formulate the DFLP using fuzzy numbers to model the
uncertainties in product market demand (Kaveh et al. 2014), transportation cost
(Samarghandi et al. 2013, Xu and Song 2015) as well as the vagueness of the closeness
relationship between facilities (Ning et al. 2010, Xu et al. 2016).
Besides the different types of formulation discussed above, Kheirkhah and
Bidgoli (2016) proposed a game theoretic model for DFLP to consider the effects of
internal and external non-cooperating competitions on the changes in facility layout
design over time, which may cause conflicts of objectives for decision makers. Bashiri
and Dehghan (2010), Bozorgi et al. (2015) and Tayal et al. (2016) established data
envelopment analysis (DEA) models for DFLP to find efficient layouts considering
several other criteria in addition to cost. For example, Bashiri and Dehghan (2010)
considered three additional criteria besides cost, including adjacency score, shape ratio
and flexibility. They used the Global Criteria method to solve the DEA model and
selected some efficient solutions for facility rearrangements.
2.2 Objectives
The objectives of FLPs generally include quantitative objectives and qualitative
objectives. Quantitative objectives aim at minimizing space cost, material handling cost,
rearrangement cost, total flow distance, traffic congestion and shape irregularities etc..
A common qualitative objective considered is maximizing adjacency rate (closeness
ratio).
In the DFLP, considering the changes in market demand, product prices and
product mix, the planning horizon is divided into multiple time periods (e.g. weeks,
months, years). Generally in DFLP, product demand, price and mix are assumed to be
deterministic and constant for each period, but change from period to period. The
product demand in each period is forecasted using historical data. Forecasts are
naturally subject to error. Therefore, to make the model more realistic, some researchers
consider the product demand to be stochastic. In these instances, the DFLP becomes the
stochastic dynamic facility layout problem (SDFLP). Studies dealing with the SDFLP
include papers of Yang and Peters (1998), Krishnan et al. (2008), Ripon et al. (2011a),
Moslemipour and Lee (2012), Tayal et al. (2016), Vitayasak et al. (2016) and Tayal and
Singh (2016). For DFLPs (including SDFLP), one common method of solving the
problem is by using adaptive layout design. In adaptive layout design, the objective is to
obtain an optimal layout for each period in the multi-period planning horizon so as to
minimizing the sum of material handling and rearrangement costs. Another way is to
use a robust approach. In a robust approach, a robust facility layout, which is not
necessarily optimal for any particular time period, is selected as the best layout over the
entire time planning horizon so that the total material handling cost is minimized
(Moslemipour et al. 2012). In recent years, the majority of DFLP studies use adaptive
layout design, while some focus on the robust approach which include work by
Krishnan et al. (2008) and Pillai et al. (2011). In addition, Yang and Peters (1998)
addressed a SDFLP and proposed a flexible machine layout design procedure which
chooses robust layout (if the machine rearrangement cost is high), adaptable dynamic
layouts (if rearrangement is easy or the production requirements change drastically), or
a combination of the two strategies.
Recently, there have been some studies that address multi-objective DFLPs
which include more than one objective. Table 2 lists all the studies of multi-objective
DFLPs. It is found that in addition to the quantitative and qualitative objectives listed at
the beginning of this section, some researchers consider other special objectives like the
flexibility of the layout, distance restriction, hazardous score etc.. For example, distance
restrictions may be required because the distance between any two departments cannot
be too large, or too small, as large distance is a waste while department overlapping can
cause great damage to the facilities as well as security problems (Jolai et al. 2012). A
‘hazardous’ score may be relevant since the relationship between the locations may
depend on the facilities safety guidelines, type of product and the working
environmental conditions so as to reduce the risk of hazard (Tayal and Singh 2016).
Specifically, as manufacturing companies become larger and diverse, Tayal and Singh
(2016) integrated Big Data Analytics (BDA) into DFLP modelling to handle and
evaluate a large set of criteria which can greatly impact the manufacturing time and
costs, product quality and delivery performance in optimal layout design. These criteria
are identified first, and a survey for generating volume, velocity and variety of Big Data
are conducted. A reduced set of criteria are then obtained using BDA. Finally, the
reduced set of criteria are used to create a mathematical model with a weighted
aggregate objective for a multi-objective SDFLP.
Table 2 DFLP with multiple objectives.
Authors Objectives
Chen and Rogers
(2009)
Minimize the total cost of material flows with consideration
of the distances between facility locations
Maximize the adjacency scores between the facilities
Bashiri and Dehghan
(2010)
All considered criteria (cost, adjacency score, shape ratio
and flexibility) are optimized through maximizing sum of
Decision Making Units' efficiencies simultaneously
Ning et al. (2010)
Minimize total handling cost of interaction flows between
the facilities associated with the construction site layout
Minimize the representative score of safety/environment
concerns.
Ripon et al. (2011a) Minimize material handling cost
Maximize closeness relationship score
Jolai et al. (2012)
Minimize material handling and rearrangement costs
Maximize total adjacency
Distance requests
Abedzadeh et al.
(2013)
Minimize material handling and rearrangement costs
Minimize shape ratio
Maximize adjacency rate
Emami and Nookabadi
(2013)
Minimize material handling and rearrangement costs
Maximize adjacency rate
Samarghandi et al.
(2013)
Minimize total transportation and shifting costs
Maximize closeness rating value
Chen and Lo (2014) Minimize material handling and rearrangement costs
Maximize closeness rating scores
Bozorgi et al. (2015) Minimize material handling and rearrangement costs
Adjacency and distance requests
Kheirkhah et al.
(2015)
Minimize total costs of material handling, buying new
material-handling devices, and idle or obsolete material-
handling devices
Minimize material handling and rearrangement costs
Xu and Song (2015) Minimize total transportation and rearrangement costs
Distance restriction
Tayal et al. (2016)
Minimize material handling and rearrangement costs, flow
distance and waste
Maximize accessibility and maintenance
Tayal and Singh
(2016)
Minimize material handling and rearrangement costs
Minimize closeness rating, material handling flow time
Maximize hazardous score
Azevedo et al. (2017)
Minimize material handling and rearrangement costs
Maximize adjacency rate
Minimize unsuitability between departments and locations
Pourvaziri and
Pierreval (2017)
Minimize average work-in-progress
Minimize empty and full trips of the material handling
system
Minimize machine rearrangement cost
2.3 Constraints
Drira et al. (2007) summarized the constraints commonly considered in FLP, which
include area constraints (space allocated and facilities’ location), position constraints
(e.g. non-overlapping, orientation and pick-up/drop-off points) and budget constraints.
Among the DFLP studies reviewed in this paper, special constraints considered in the
model mainly include non-overlapping constraints, orientation constraints, pick-
up/drop-off points constraints, budget constraints and capacity constraints. The capacity
constraint considered in the literature usually refers to the limitation on machine
capacity (Kia et al. 2013, Kia et al. 2015). The DFLP studies with special constraints are
summarized in Table 3.
Table 3 DFLP with different constraints.
Constraints Authors
Non-overlapping
Yang and Peters (1998), Corry and Kozan (2004), Dunker et
al. (2005), McKendall Jr and Hakobyan (2010), Jolai et al.
(2012), Abedzadeh et al. (2013), Mazinani et al. (2013),
Derakhshan Asl and Wong (2015), Kia et al. (2015),
Kulturel-Konak and Konak (2015), Wang et al. (2015), Xu
and Song (2015)
Orientation Yang and Peters (1998), Dunker et al. (2005), Jolai et al.
(2012), Abedzadeh et al. (2013), Kia et al. (2015)
Pick-up/drop-off
points Dunker et al. (2005), Jolai et al. (2012), Kia et al. (2015)
Budget Baykasoglu et al. (2006), Şahin et al. (2010), Azimi and
Charmchi (2012), Li et al. (2015)
Capacity Kia et al. (2013), Kia et al. (2015)
2.4 Facility characteristics
Layout problems addressed are also dependent on specific characteristics of the facility
studied. Several factors and design issues clearly differentiate the nature of DFLPs
addressed, including different manufacturing systems, layout configurations, and
facility shapes.
Drira et al. (2007) categorized manufacturing systems into four types based on
products variety and the production volumes, which include fixed product layout,
product layout, process layout and cellular layout. The fixed product layout is often
adopted by industries manufacturing large size products (e.g. ships, aircrafts, etc.),
where the product does not move, while different resources and facilities are moved to
perform operations on the product. More commonly, products circulate within various
production facilities (e.g. machines, workers, etc.). When the manufacturing system has
high production volume and low variety of products, facilities are organized according
to the order of the successive manufacturing operations, which is called a product
layout. When product variety is high or production volume is low, process layout
(functional layout) is a common choice, in which resources of the same type (facilities
with similar functions) are grouped together. Process layout is often thought to provide
the greatest flexibility, but is notorious for its inefficient material-handling and complex
scheduling, which can result in long lead times and large work-in-process inventories
(Benjaafar et al. 2002). Cellular layout is an alternative to a process layout. In cellular
layout, the factory is partitioned into cells, and each cell is dedicated to a family of
products with similar processing requirements (Heragu 1994). Although cellular layout
can simplify work flow and reduce material handling, it is inefficient when demand for
existing products fluctuates or new products are introduced often (Benjaafar et al.
2002). For cellular layout, researchers are generally concerned with not only the inter-
cell layout problem, but also the intra-cell machine layout problem. In the recent DFLP
studies, Shahbazi (2010) and Yang et al. (2011) specifically focused on process layout
problem, and a few other researchers work on cellular layout problems (see Table 4).
Table 4 DFLP for cellular layout.
Manufacturing System Authors
Cellular Layout Chen (1998), Kia et al. (2012), Kia et al. (2013), Kia et al.
(2014), Kia et al. (2015), Kumar and Prakash Singh (2017)
Layout configuration is another design issue that impacts the DFLP. Most of the
recent models regarding DFLPs are formulated using modified QAP, which is one of
the many dealing with multi-row layout problems. The multi-row layout problem
locates facilities on several rows and each pair of facilities is separated by their
minimum clearances. In particular, Wang et al. (2015) solved a dynamic double-row
layout problem. Besides multi-row layout problems, some researchers are interested in
single-row layout optimization. Chan and Malmborg (2010) addressed a dynamic line
layout problem. Tayal and Singh (2016) focused on optimizing the U-shape facility
layout, which is also a type of single-row layout problem. Nowadays, with land supply
being insufficient and land being expensive, manufacturers may seek to locate the
facilities on several floors, so as to overcome the limitation on available horizontal
space in the facility. This leads to the multi-floor FLP. In the multi-floor FLP, both the
position on the floor and the level of the floor have to be determined for each facility.
Additionally, material flow in multi-floor FLP has two directions, since the products
can move both horizontally on a given floor (horizontal flow) and vertically from one
floor to another floor at a different level (vertical flow), all of which need to be
considered in finding the optimal solution. In the DFLP studies reviewed in this paper,
Kochhar and Heragu (1999) and Kia et al. (2014) solved dynamic multi-floor FLPs.
Facility shapes are divided into two types: regular shape (i.e., generally
rectangular) and irregular shape. For regular facility shape, the rectangular facility can
be defined by fixed dimensions, i.e., fixed length (𝐿𝑖) and fixed width (𝑊𝑖), or by its
area using aspect ratio. Aspect ratio is usually defined by 𝑎𝑖 = 𝐿𝑖 𝑊𝑖⁄ , with an upper
bound 𝑎𝑖𝑢 and a lower bound 𝑎𝑖𝑙 such that 𝑎𝑖𝑙 ≤ 𝑎𝑖 ≤ 𝑎𝑖𝑢. The facility shape is fixed if
𝑎𝑖𝑙 = 𝑎𝑖 = 𝑎𝑖𝑢. In the DFLPs reviewed, a majority of the studies consider a regular
rectangular facility with fixed dimensions, while a few studies define facility shape
through the aspect ratio (see Table 5).
Table 5 DFLP with aspect ratio.
Regular Facility Shape Authors
Aspect Ratio
Kulturel-Konak et al. (2007), Bashiri and Dehghan (2010),
Abedzadeh et al. (2013), Mazinani et al. (2013), Kulturel-
Konak and Konak (2015)
3 Solution methodology
Solution methods for DFLP can be grouped into four categories: exact methods,
heuristics, metaheuristics, and hybrid approaches. As the DFLP is NP-hard, exact
(optimal) methods are only useful in finding optimal solutions for small-sized problems.
In recent years, very few DFLP studies have adopted exact methods, while most of the
effective algorithms found in the DFLP literature are heuristics, metaheuristics and
hybrid approaches. Studies using different exact methods, heuristics, metaheuristics and
hybrid methods are summarized in Table 6.
3.1 Exact methods
The three types of exact methods used in recent DFLP studies are branch-and-bound,
dynamic programming and modified sub-gradient.
3.1.1 Branch-and-bound
Branch-and-bound (B&B) is one of the most commonly used tool for solving NP-hard
optimization problems. In the B&B algorithm, at each iteration, the current problem is
branched into smaller subsets, and the lower bound (in the case of minimization) on the
cost of all possible solutions within each subset is calculated. A branch is pruned, if it
cannot produce a better solution than the best one found so far by the algorithm.
Eventually, the optimal solution (if any) is found when all branches have been pruned.
Lahmar and Benjaafar (2005) provided an exact solution based on B&B procedure for
small-sized multi-period distributed layout problems, where product mix may vary from
period to period and a re-layout can be undertaken at the beginning of each period.
3.1.2 Dynamic programming
In dynamic programming (DP), to solve a DFLP with 𝑛-facility and 𝑡-period, a very
large number (𝑛!)𝑡 of possible solutions must be evaluated to find the optimum
solution. For example, we would have to evaluate 1.93 × 1014 possible solutions for a
six-facility and five-period DFLP. Hence, DP is used only to solve small-sized DFLPs.
Chen (1998) proposed a facility layout model for designing sustainable cellular
manufacturing systems with anticipated changes of demand or production process. This
model attempts to minimize the total of inter-cell traveling cost, machine cost, and
machine installation/removal cost. To solve this problem, DP was employed and a
decomposition approach was developed so that the decomposed sub-problems can be
solved with less computational effort. Urban (1998) used an incomplete DP algorithm
similar to that of Wesolowsky’s (1973), so as to find the optimal solution for a special
case of DFLP where the rearrangement cost is fixed.
3.1.3 Modified sub-gradient
Ulutas and Saraç (2012) solved a DFLP using the modified sub-gradient (MSG)
algorithm for the first time. The MSG algorithm was proposed by Gasimov (2002) for
solving a continuous non-linear model. Therefore, to apply the MGS algorithm, the
modified QAP model for DFLP was converted into the continuous form first. Since the
performance of the MSG algorithm depends on parameters and solver type, the authors
also designed computational experiments to determine the appropriate parameter values
and the most suitable SNOPT solvers in the general algebraic modelling system
(GAMS) software used for solving the problem. The experimental analysis results
showed that when suitable parameters are chosen, the MSG algorithm is a promising
and competitive algorithm for solving DFLP; and the solver type has more influence on
large scale problems.
3.2 Heuristic algorithms
Solving DFLP is a computationally difficult task, exact approaches are often considered
not suitable for large-sized problems. As a result, many researchers developed heuristics
and metaheuristics to solve large scale DFLPs. Heuristics are also called sub-optimal or
approximated approaches, which can produce near-optimal satisfactory solutions in a
very low computational time for problems where finding an optimal solution is
impossible or impractical.
In addition to the incomplete DP algorithm, Urban (1998) also introduced
heuristic methods for problems with larger scale. In addition, upper and lower bounds
that dominate all existing bounds were developed for the general DFLP where the
rearrangement cost is not necessarily fixed. Yang and Peters (1998) proposed a heuristic
procedure based on a construction type layout design algorithm to solve a flexible
machine layout design problem over a planning horizon. Balakrishnan et al. (2000)
developed an improved dynamic pair-wise exchange heuristic for DFLP. Their heuristic
is on the basis of the steepest descent pairwise exchange heuristic proposed by Urban
(1993) with two improvements. The first one is using a backward pass instead of the
forward pass in Urban’s (1993) heuristic because the backward pass will never generate
a worse layout than the forward pass (Kulturel-Konak 2007). The second one involves
combining Urban’s (1993) method with the DP proposed by Rosenblatt (1986). They
tested the new dynamic pair-wise exchange heuristic on different problems, and showed
improvements on the results published by Urban (1993) in almost every case.
Balakrishnan and Cheng (2009) also investigated the performance of this improved
dynamic pair-wise exchange heuristic under fixed and rolling horizons, under different
shifting costs and flow variability, and under forecast uncertainty. The results showed
that rolling horizons have significant effect on the algorithm performance, while
forecast uncertainty may not significantly affect the algorithm effectiveness and may be
beneficial in some cases. Additionally, it is difficult to identify an algorithm that
performs well under all situations (Balakrishnan and Cheng 2009). Ripon et al. (2011a)
also developed a modified version of Urban’s (1993) heuristic by incorporating a
backward pass to solve the multi-objective DFLP under uncertainty that presents the
layout as a set of Pareto-optimal solutions.
In addition to an exact method, Lahmar and Benjaafar (2005) offered a
decomposition-based heuristic solution procedure for distributed layout design in
settings with multiple periods where product demand and product mix may vary from
period to period and where a re-layout may be undertaken at the beginning of each
period. They showed that the proposed heuristic performs well relative to lower bounds.
Also, as a distributed layout is quite robust to uncertainties in the production
requirements, optimizing the layout in each period carries significantly less value than it
does for process layouts. Chan and Malmborg (2010) developed a simple Monte Carlo
simulation based heuristic procedure to identify robust solutions for dynamic line layout
problems in which the production facility has unequal size work centres, uses
conventional material handling devices and operates under stochastic demand scenarios.
Their experimental results showed that robust solutions meeting aspiration levels of
material handling cost performance across multiple material flow scenarios can be
obtained using a modest volume of random sampling.
Recently, Kumar and Prakash Singh (2017) introduced a novel similarity score-
based two-phase heuristic approach which can optimally solve the dynamic cellular
layout problem considering multiple products in multiple times to be manufactured
within reasonable time. In this two-phase heuristic, first, machines are grouped in cells
in Phase I through using a grouping algorithm based on similarity score of machines in
the machine–part matrix. In Phase II, an integer programming DFLP is formulated for
the cellular layout problem. The proposed heuristic method was able to obtain
promising solutions for the tested dynamic cellular FLP in reasonable time.
3.3 Metaheuristics
‘A metaheuristic is a set of algorithmic concepts that can be used to define heuristic
methods applicable to a wide set of different problems’ (Dorigo et al. 2006). Since the
DFLP is NP-hard, in recent years, a large number of researchers have used efficient
metaheuristics to solve the DFLP, especially for large-sized problems. The popular
metaheuristics used in DFLP studies mainly include simulated annealing, tabu search,
genetic algorithm, ant colony optimization, particle swarm optimization, artificial
immune system, and fuzzy system and so on.
3.3.1 Simulated annealing
Simulated annealing (SA) was first proposed by Kirkpatrick et al. (1983) which
originates from the theory of statistical mechanics and is based on the analogy between
the annealing process of solids and the solution methodology of combinatorial
optimization problems (Baykasoğlu and Gindy 2001). SA is relatively easy to
implement and is free of local optima in global optimization. However, the quality of
the solution obtained by SA depends on the maximum iteration number of the inner
loop (cooling schedule) and the initial temperature (Moslemipour et al. 2012). In recent
years, SA has been a commonly used metaheuristic for solving DFLP.
After Baykasoğlu and Gindy (2001) first applied the SA to DFLP, McKendall Jr
et al. (2006) developed two SA heuristics for DFLP, one is a straightforward adaptation
of SA to DFLP, the other combines the first SA method with a look-ahead/look-back
strategy. After testing the two SA methods with the data sets taken from the study of
Balakrishnan and Cheng (2000), the results showed that the proposed SA heuristics
perform well. Ashtiani et al. (2007) proposed a multi-start SA to solve the DFLP.
Compared with the SA heuristic developed by Baykasoğlu and Gindy (2001) and the
hybrid genetic algorithm presented by Balakrishnan et al. (2003), the results showed
that the multi-start SA performs well. Dong et al. (2009) presented a new DFLP with
the capability of removing/adding machines in different periods. This new DFLP is
defined based on unequal area machines and continual representation, which was
converted to a shortest path problem. A shortest path based SA algorithm was proposed
to solve this new DFLP. Tests with a case of four periods and 56 machines, showed that
the proposed SA algorithm is efficient and effective. Later, Şahin et al. (2010)
developed a SA for DFLP considering a budget constraint.
Recently, Pillai et al. (2011) presented a robust model for DFLP. A SA heuristic
was proposed to solve the suggested robust model, which performs well in almost all
cases of problems from Yaman et al. (1993) and the QAPIB website, except in one case
where the result is inferior by 0.07% compared with the optimal value. Kia et al. (2012)
established a novel non-linear MIP model integrating cell formation and group layout
decisions for a dynamic cellular layout problem. The presented model incorporates
several design features including alternate process routings, operation sequence,
processing time, production volume of parts, purchasing machines, duplicate machines,
machine capacity, lot splitting, intra-cell layout, inter-cell layout, multi-rows layout of
equal area facilities and flexible reconfiguration (Kia et al. 2012). A SA technique was
developed to solve the model. The solution structure of the SA is presented as a matrix
consists of four ingredients fulfilled hierarchically to satisfy constraints. The
performance of the proposed SA algorithm is evaluated and compared with the LINGO
software using several small/medium-sized problems. The results showed that the
proposed SA algorithm could find near-optimal solutions in computational times
approximately 100 times less than that of LINGO (Kia et al. 2012). Later, Kia et al.
(2015) applied a SA heuristic to another dynamic cellular layout problem, which also
integrates cell formation and group layout decisions but considers variability in the
number and shape of cells. Kia et al. (2013) proposed a non-linear MIP model for intra-
cell layout design of a dynamic cellular manufacturing system, which aims to minimize
the total costs of inter-cell material handling, forward and backward intra-cell material
handling, setting up routes, machine relocation, purchasing new machines, as well as
machine overhead and processing. The proposed model was solved by a SA algorithm
whose solution structure was presented as a matrix with six ingredients fulfilled
hierarchically to satisfy constraints.
Moslemipour and Lee (2012) presented a model for dynamic layout design of a
flexible manufacturing system in an uncertain environment where the product demands
are assumed to be independent normally distributed random variables with a known
probability density function and change from period to period. The model also considers
the decision maker’s attitude about uncertainty in product demands using different
confidence levels. A SA method with three different confidence levels was adopted to
solve two test problems with 10 parts, 12 machines and two different time periods.
Optimal layouts for both of the two test problems were obtained in a reasonable
computational time. Li et al. (2015) focused on DFLP for remanufacturing, where a
high-level uncertainty exists due to the stochastic returns of used products or
components and uncontrollable quality conditions. They proposed a dynamic multi-row
layout model and utilized a modified SA approach as the solution method which has a
special solution structure with two-stage matrices for remanufacturing layout schemes.
Kheirkhah and Bidgoli (2016) developed a game theoretic model for DFLP which
considers the effect of an external duopoly Bertrand competition on the facility layout
designs under a changing environment. Three algorithms were proposed to evaluate this
game theoretic model which include B&B, SA and an imperialist competitive algorithm
(ICA). Computational results showed that the proposed SA outperforms other proposed
algorithms. Tayal et al. (2016) investigated a sustainable SDFLP considering several
quantitative and qualitative criteria, namely material handling cost, rearrangement cost,
flow distance, accessibility, maintenance and waste management. The proposed
sustainable SDFLP was optimized using various metaheuristic techniques which include
SA, chaotic simulated annealing (CSA) and hybrid firefly-chaotic simulated annealing
(Hybrid FA/CSA). The layouts generated by SA, CSA and Hybrid FA/CSA were then
used to identify efficient layouts through DEA. Finally, multiple attribute decision
making (MADM) techniques and consensus ranking method were applied to rank the
efficient layouts considering the aforementioned six criteria. Pourvaziri and Pierreval
(2017) presented a DFLP that focuses on reducing not only the material handling and
rearrangement costs but also the amount of work-in-process. A cloud-based multi-
objective simulated annealing (C-MOSA) which takes advantage of both a Pareto
approach and cloud theory was used to find the Pareto-optimal solutions. After
comparing the C-MOSA with parallel variable neighbourhood search (PVNS) and non-
dominated sorting genetic algorithm (NSGA-II), it showed that the C-MOSA performs
better than PVNS and NSGA-II in terms of two performance criteria, mean ideal
distance and diversity. Performance of C-MOSA is also acceptable with regard to
spacing.
3.3.2 Tabu search
Developed by Glover (1989, 1990), tabu search (TS) is a metaheuristic featured by
incorporating two main strategies in local search: adaptive memory and responsive
exploration. The basic principle of TS is to prevent cycling back to previously visited
solutions through using memory (tabu list) which stores the recent search history; and to
accept non-improving moves so as to escape from a local optimum and explore a larger
fraction of the search space to find global optimum.
To the best of our knowledge, the first study adopted TS to solve DFLP was by
Kaku and Mazzola (1997). In their TS approach, they used pairwise interchange as the
local neighbourhood search technique. Their TS heuristic employs two stages. In the
first stage, initial solutions are generated using a diversification strategy. In the second
stage, neighbourhoods around the promising solutions found in the first stage are
searched more intensively. At the end of the second stage, the best layout for DFLP is
obtained by the TS heuristic. Compared with some existing heuristics, computational
experiment results showed that the proposed TS generates improved solutions for over
one third of the test problems. Kulturel-Konak et al. (2007) studied a facility re-layout
problem considering unequal area redesign including both fixed facility areas and
expanded facility areas. The proposed bi-objective model aims at minimizing material
handling cost and re-layout cost was solved by a TS heuristic. In this TS heuristic, the
objective function can randomly alternate between the two objectives in each step,
thereby eliminating the difficulty of weighting and scaling the two objectives. Test
results showed that the proposed TS heuristic is an effective and computationally
tractable algorithm. McKendall and Jaramillo (2006) studied the dynamic space
allocation problem (DSAP) which can be regarded as a generalization of both the QAP
and the DFLP. They used a TS approach and five construction algorithms to solve the
DSAP. The five construction algorithms include the first assignment algorithm (FA),
the randomized clustering algorithm (RC), the modified first assignment algorithm
(MFA) and two modified RC algorithms (MRC I, MRC II). These five construction
algorithms are also used to generate initial solutions for the TS heuristic. It was shown
that the TS heuristic with MFA, MRC I and MRC II outperformed the TS heuristic with
FA and RC with respect to both solution quality and computational time. The proposed
TS heuristic also performs better than the SA heuristics presented in the literature.
Later, McKendall Jr (2008) developed another three TS heuristics for the DSAP. The
first TS is a simple basic TS which is an improvement of the TS in the paper of
McKendall and Jaramillo (2006); the second TS is the proposed simple basic TS with
diversification and intensification strategies added; the third TS is a probabilistic TS.
Tests showed that all the three TS heuristics are efficient techniques for solving the
DSAP, while the TS with diversification and intensification strategies can find new best
solutions using less computational time for half of the test problems. McKendall Jr and
Hakobyan (2010) presented a continuous DFLP in which the departments have unequal-
areas, fixed department shapes and free orientations. A boundary search (construction
type) technique (BSH) and a TS (improvement type) technique (TS/BSH) using BSH to
generate initial solutions were developed to solve the problem. The computational
results showed that TS/BSH heuristic performs well, especially for the large-sized
problems. Shahbazi (2010) investigated the DFLP for the case of job shop process and
added a new aspect to the problem, which is considering time value of money. To solve
this new DFLP, SA and TS heuristics were developed. The computational experiments
showed that the proposed TS heuristic performed better than the SA heuristic.
McKendall Jr and Liu (2012) developed three TS heuristics for DFLP. Similar to
McKendall Jr (2008), the three TS heuristics included a simple basic TS, the proposed
simple basic TS with diversification and intensification strategies added and a
probabilistic TS. It was shown that the TS with diversification and intensification
strategies had the best performance. Bozorgi et al. (2015) determined the most efficient
layout for DFLP with equal departments considering three criteria: cost, adjacency rate,
and distance requested. For this purpose, a DEA model and a TS heuristic with
diversification strategy including frequency-based memory, penalty function and
dynamic tabu list size were applied. The local search technique used in the proposed TS
heuristic is the steepest descent pairwise exchange heuristic. In the DEA model, cost is
a negative criterion which needs to be minimized and is used as the input, whereas
adjacency and distance requested are taken as positive criteria and used as outputs.
Computational results showed that the proposed TS heuristic performs better than other
heuristics developed in relevant literature, and the most efficient layout was obtained.
3.3.3 Genetic algorithm
Genetic algorithm (GA) is a metaheuristic inspired by the evolutionary ideas of natural
selection and genetics. GA starts with an initial set of random solutions known as the
‘population’. The individual solutions in the population are called ‘chromosomes’. The
initial population evolves into an optimal solution through successive iterations called
‘generations’. In each generation, a new population is created through merging
(crossover) and modifying (mutation) chromosomes of the existing population. The
selection of chromosomes to crossover and mutate is based on their fitness function (El-
Baz 2004). These iterations continue until the GA finds an acceptably good solution
(Kia et al. 2014).
Kochhar and Heragu (1999) studied a multiple-floor unequal-area DFLP which
is able to respond to production demand and mix changes in a continuously evolving
environment. They proposed a GA-based heuristic to solve this problem. Balakrishnan
and Cheng (2000) developed a GA with nested loops to solve large-sized DFLPs. In this
GA approach, they used point-to-point crossover to increase the search space. To
increase population diversity, they utilized mutation and a generational replacement
approach. The computational experiment results showed that the proposed GA
outperforms the one developed by Conway and Venkataramanan (1994). Krishnan et al.
(2008) presented a mathematical model to determine a compromise layout that can
minimize the maximum loss in material handling cost for both single and multiple
periods. The proposed model is then modified to minimize the total expected loss. A
GA approach was developed to solve the proposed models. Results from the case
studies showed that the compromise layouts obtained can efficiently reduce maximum
loss in material handling cost and minimize the total expected loss.
Yang et al. (2011) adopted a GA approach to solve a dynamic layout planning
model considering job order as it significantly affects the moving paths of materials in a
job shop manufacturing environment. This study also applies the cost-benefit analysis
based on the cost gap between the current layout and the ideal layout obtained by GA. It
was suggested that changing the layout can be a good choice when the rearrangement
cost is lower than the cost gap. Emami and Nookabadi (2013) presented a multi-
objective model for DFLP which aims at minimizing material handling and
rearrangement costs and maximizing adjacency rate. They evaluated two classic
methods (weighted sum and ε-constraint methods) and three metaheuristic methods
including nondominated sorting GA (NSGA-II), differential evolution (DE) and Pareto-
simulated annealing (PSA), in which only DE had not been applied to solve the multi-
objective DFLP. Using the technique for order performance by similarity to ideal
solution (TOPSIS), the best method was selected on the basis of three comparison
criteria (i.e. convergence, diversity and runtime). It was shown that metaheuristics
outperform classic methods, and NSGA-II and DE are more efficient than PSA.
Mazinani et al. (2013) proposed a novel DFLP based on flexible bay structure. In this
new DFLP, departments may be free oriented and have unequal areas, which are
assigned to parallel bays in a plant floor. A GA was established to solve this problem.
After being tested on some problems taken from existing literature, the proposed GA
was shown to be effective compared with other algorithms and software. Besides the
SA methods discussed previously, Kia et al. (2014) also developed an efficient GA with
a matrix-based chromosome structure to solve the multi-floor dynamic cellular layout
problem that integrates cell formation and group layout decisions and aims at
minimizing the total costs of intra-cell, inter-cell, and inter-floor material handling,
purchasing machines, machine processing, machine overhead, and machine relocation.
Vitayasak et al. (2016) solved a SDFLP with heterogeneous-sized resources and
rectilinear material flow using three modified Backtracking Search Algorithms
(mBSAs), the classic Backtracking Search Algorithm (BSA) and GA. BSA is a new
evolutionary algorithm which has a simple structure and a single control parameter.
BSA’s strategies (two new crossover and mutation operators) for generating trial
populations and controlling the amplitude of the search-direction matrix and search-
space boundaries make its exploration and exploitation capabilities very powerful
(Civicioglu 2013).
3.3.4 Ant colony optimization
The fundamental idea of ant colony optimization (ACO) is on the basis of the social
behaviour of natural ants succeed in finding the shortest path from the nest to the food
source through following the path with strong pheromone concentration. Pheromone is
a volatile chemical substance laid by ants when they move along randomly selected
paths. Over time, pheromone on the trail starts to evaporate, thus reducing its
concentration. As it takes more time for ants to travel down and back on long paths,
more pheromone evaporates, while on short paths, more ants can make the return trip in
a given amount of time, thereby increases the density of pheromone and attracts more
ants traveling on this path. Eventually, pheromone on the shortest path dominates all
other paths, thus most ants are travelling on the shortest path from nest to food source
(Corry and Kozan 2004).
Different ACO algorithms have been applied to the DFLP studies in recent
years. Corry and Kozan (2004) introduced an ACO algorithm to solve DFLP with fixed
shape. The proposed ACO was shown to outperform the heuristically reduced integer
programming method used in the study by Yang and Peters (1998). Baykasoglu et al.
(2006) used an ACO to solve a DFLP considering the unconstrained and budget
constrained cases. This study is the first attempt that applies ACO to DFLP with a
budget constraint. Ning et al. (2010) proposed a new solution approach using max-min
ant system (MMAS) under the guidance of continuous dynamic searching scheme to
solve the multi-objective dynamic construction site layout planning problem through a
weighted sum method. Chen and Lo (2014) studied the multi-objective DFLP with
distance-based and adjacency-based objectives. They combined ACO with three
different multi-objective approaches to solve this problem. The first approach is called
ACO-DDML, which couple the ACO with MUGHAL, a weight-sum method for
solving FLPs proposed by Dutta and Sahu (1982). The second approach, named ACO-
UDML, combines ACO with the additive model developed by Urban (1987). This
approach determines the relative importance of the adjacency-based objective to the
distance-based objective relying on only one user-defined weight. The third approach
ACO-PDML coupling ACO with the Pareto efficiency concept, does not assign weights
for multiple objectives but searches for a set of non-dominated solutions. The evaluation
results showed that all the three proposed approaches are effective in solving the
problem, however none of the them dominates the others for both of the two objectives.
3.3.5 Particle swarm optimization
Particle swarm optimization (PSO) is a population-based stochastic optimization
approach motivated by the analogy with the social behaviour of bird flocking or fish
schooling. It belongs to evolutionary computation techniques which shares many
similarities with ACO and GA. PSO operates with a population (swarm) of candidate
solutions (particles). In PSO, particles fly through a multidimensional search space to
find the optimal solution. The position of each particle is considered as a solution for
the problem. During the flight, the new position of each particle is guided by the best
position found by the particle and the entire swarm's best-known position. Since
particles in PSO naturally move in continuous space, it is fundamentally designed to
solve continuous problems.
Jolai et al. (2012) dealt with a multi-objective DFLP with unequal sized
departments and pick-up/drop-off locations. To solve the problem, they proposed a
multi-objective PSO together with two novel heuristics used to preventing departments
overlapping and reducing unused gaps between departments. Computational experiment
results showed that the average percentage improvements over the initial solutions of
the proposed multi-objective PSO ranges between 2% and 24% for the four objectives
considered in the problem. Xu and Song (2015) developed a multi-objective position-
based adaptive PSO (p-based MOPSO) to solve a multi-objective DFLP with unequal-
area departments and fuzzy transportation cost for temporary construction facilities. The
main difference between the proposed p-based MOPSO and the standard PSO is in
solution representation. The p-based MOPSO uses a position-based solution
representation, in which the multidimensional particles with different position values for
each dimension are used to represent the candidate solutions (Xu and Song 2015).
Kheirkhah et al. (2015) investigated a DFLP which is strongly correlated with the
material handling system (MHS) design problem. A novel bilevel model was proposed
for this problem, in which the upper objective function minimizes the total costs of
material handling between departments, buying new material-handling devices (MHDs)
and idle or obsolete MHDs; while the lower level objective function minimizes the total
costs of material handling and rearrangement. Two bilevel metaheuristics known as
bilevel PSO and coevolutionary algorithm were developed to solve the proposed bilevel
model. Compared with the coevolutionary algorithm, the computational results showed
that the bilevel PSO gives better average upper level fitness, better rationality and can
solve the problem in shorter computational time. Derakhshan Asl and Wong (2015)
applied a modified PSO to solve both the static facility layout problem (SFLP) and
DFLP with unequal area. In this modified PSO, two local search methods are used.
Additionally, the department swapping method is also adopted to prevent local optima
and improve the quality of solutions.
3.3.6 Artificial immune system
Artificial immune system (AIS) is an evolutionary computation technique inspired by
the principles and processes of the human immune system. Mechanisms and properties
of immune system such as the clonal selection, learning ability, memory, robustness,
and flexibility make AIS an efficient tool for solving combinatorial problems. The AIS
technique that has been applied to the DFLP is the clonal selection algorithm (CSA)
which is a population-based algorithm. In CSA, feasible solutions are coded as
individuals. CSA starts with a randomly generated population of individuals
(antibodies). At each iteration of CSA, first, the affinity value of each antibody is
calculated by using the problem’s objective function. Then, the antibodies with the best
affinity value are selected and cloned. Next, the new generations which are the
improved antibodies created by mutating the clones are formed. Finally, a
predetermined number of antibodies with low affinity value are replaced by the
randomly generated new ones through the receptor editing process. The CSA terminates
after replicating a pre-specified number of generations.
Ulutas and Islier (2009) proposed a CSA to solve the DFLP. Test results showed
that the proposed CSA achieves the best-known solutions and even better solutions for
large-sized problems in nearly 90% of the cases. The CSA also outperforms other
methods in the literature with regard to computation time. Later, Ulutas and Islier
(2010) adopted the DFLP model proposed by Balakrishnan et al. (2003) (see Eq. (1)-
(4)) to solve the dynamic content area layout for internet newspapers. The objective of
this layout problem is to minimize the sum of the content dissimilarities (material
handling cost) and permanence values (rearrangement cost) for the planning horizons.
This layout problem is optimized by CSA as well. Ulutas and Islier (2015) also used the
CSA to solve a real-life DFLP in the footwear industry which is prone to seasonal
demand changes. To the best of our knowledge, it is the first study of a real-life
application.
3.3.7 Fuzzy system
Fuzzy logic uses the whole interval between 0 (false) and 1(true) to describe human
reasoning. A fuzzy decision-making system consists of four major components,
including fuzzification, knowledge base (including membership functions), if-then
fuzzy decision rules, and defuzzification (Moslemipour et al. 2012). Fuzzy logic is an
efficient method to cope with uncertainties in DFLP. Ning et al. (2010) and Xu et al.
(2016) utilized fuzzy logic to represent the closeness relationship. In their studies, the
closeness rating between facilities is divided into five levels described by linguistic
words: absolutely important (A), especially important (E), important (I), ordinary (O),
unimportant (U) and undesirable (X). Samarghandi et al. (2013) investigated a fuzzy
multi-objective DFLP with unequal areas. They modelled the amount of transportation
between two facilities using triangular fuzzy numbers. In order to solve this problem,
several algorithms including a fuzzy TS, a fuzzy GA, a fuzzy PSO and a fuzzy variable
neighbourhood search (VNS) were developed. Kaveh et al. (2014) defined the product
demand in DFLP as fuzzy numbers with different membership functions. Therefore,
material handling cost, and consequently the total costs are fuzzy numbers as well. The
DFLP is then modelled as fuzzy programming through three approaches including
expected value model (EVM), chance-constrained programming (CCP) and dependent-
chance programming (DCP). As decision makers can only provide a range for average
unit cost of materials transportation and the transportation cost fluctuates over time, Xu
and Song (2015) modelled the transportation costs between the facilities as fuzzy
random variables.
3.3.8 Other metaheuristics
Urban (1998) adopted a greedy randomized adaptive search procedure (GRASP) and an
initialized multigreedy algorithm to solve the large-sized DFLP with fixed
rearrangement cost. Each iteration in GRASP consists of two phases including
randomized construction and local improvement. In the construction phase, an initial
feasible solution is randomly selected from a list of the most promising assignments.
After a feasible solution is generated, a local search is conducted to identify better
solutions in the improvement phase. Finally, at the end of all iterations, the best solution
obtained is taken as the final solution. The initialized multigreedy algorithm is similar to
GRASP, but appropriate information is transferred between sub-problems in it. The test
results showed that for problems with 20 departments or less, the GRASP obtains better
solutions than the initialized multigreedy algorithm with slightly higher computational
time; while for larger problems, solutions provided by the initialized multigreedy
algorithm have better quality, but the GRASP uses shorter computational time.
Ming et al. (2002) developed a symbiotic evolutionary algorithm (SymEA) to
solve the DFLP. In this SymEA, a coevolutionary multi-population approach is
implemented, hence layouts of a particular period are represented as individuals of a
corresponding population. A complete solution, called a symbion, is a combination of
individuals in different populations. Symbion is the unit in the evaluation and selection
process, top ranked symbia are used to reproduce the population for the next generation.
Hence, populations evolve simultaneously and individuals interact both in evaluation
and selection process (Ming et al. 2002). In addition, the generational replacement
strategy (𝜇, 𝜆)-selection derived from Evolution Strategies was adopted for refining the
symbiotic relationship. It was shown that the proposed SymEA has better performance
than other proposed GAs, but is outperformed by a SA algorithm in large-sized
problems.
Abedzadeh et al. (2013) solved the multi-objective DFLP using a parallel
variable neighbourhood search (PVNS) algorithm and CPLEX 12 optimizer for GAMS
23.3 software. In the proposed PVNS algorithm, six structures, namely ‘swap,
reversion, perturbation, insertion, exchange variable and 2-Opt algorithm’ were adopted
for producing the neighbourhood around each solution (Abedzadeh et al. 2013). Test
results showed that that the proposed PVNS algorithm is more efficient than GAMS
software.
Kheirkhah and Bidgoli (2016) evaluated a game theoretic model for DFLP using
BB, SA and ICA. ICA is a metaheuristic inspired by the socio-political competition
among empires in human social evolution. The proposed ICA has the shortest
computation time but cannot get good quality solutions because its performance is
largely dependent on the initial solutions.
3.4 Hybrid algorithms
Hybrid algorithms, which combine two or more solving methods together to further
enhancing their computational capabilities have drawn increasing attention among
researchers in recent years.
GA is commonly considered in hybrid approaches. Balakrishnan et al. (2003)
proposed a hybrid GA for DFLP using DP in crossover to create offspring and using a
pair-wise exchange heuristic named CRAFT as the mutation method. Compared to
other methods, it showed that the proposed hybrid GA performs better than the GA
methods developed by Conway and Venkataramanan (1994) and Balakrishnan and
Cheng (2000) as well as a SA. Dunker et al. (2005) developed a hybrid algorithm
combining DP and GA to solve DFLP with unequal area. Krishnan et al. (2006)
established a new tool called Dynamic From-Between Charts (DFBC) to capture the
dynamic inter-departmental relationship and continuously track the flow between
machines in DFLP. Besides, they proposed an algorithm which uses a modified
Wagner-Whitin (W-W) procedure to select the redesign point and a GA to determine
the layout at each step of the algorithm. Lately, since there is increasing use of industrial
robots as material handling devices, Ripon et al. (2011b) established a hybrid GA
incorporating jumping genes operations and a modified backward pass pair-wise
exchange heuristic to solve the DFLP, so as to enhance the production rate and profit,
save robot energy usage and extend the life of the robot. The GA with jumping genes
operations has better capability of exploration and exploitation because it employs
horizontal transmission together with the vertical transmission in the conventional GAs.
Experimental results indicated that the proposed hybrid GA performs well in solving
DFLP. Pourvaziri and Naderi (2014) developed a novel hybrid multi-population GA for
DFLP, which overcomes the shortcomings of the existing algorithms and further
improves the performance. In this hybrid GA, the subpopulation is generated using a
heuristic procedure which ensures the diversification capability. A powerful SA-based
local search is allocated to enhance the intensification capability. They also proposed a
novel crossover operator generating only feasible solutions to reduce computational
time. Comparing the hybrid multi-population GA with 11 other available algorithms, it
showed that the proposed algorithm outperforms all the others. Uddin (2015) developed
a hybrid metaheuristic GA-VNS for the DFLP which elegantly integrates the
exploration ability of GA and the exploitation ability of VNS together. In the proposed
hybrid algorithm, GA is used to ensure diversification capability and VNS local search
is applied for intensification. Besides, in VNS, different neighbourhood structures are
included to avoid getting trapped into local optimal and expand the search scope.
SA is another frequently adopted metaheuristic in hybrid methods. Şahin and
Türkbey (2009) presented a hybrid algorithm named TABUSA, which adopts both the
stochastic nature of the SA and the short-term memory of TS (tabu list) to solve the
DFLP. They compared the performance of TABUSA with pure SA and pure TS and
showed that the proposed TABUSA is a very effective method to solve the DFLP.
Kulturel-Konak and Konak (2015) developed a large-scale hybrid algorithm (LS-HSA)
based on the hybridization of SA and MIP to find good solutions for the cyclic facility
layout problem (CFLP), which is a special case of DFLP. Wang et al. (2015) combined
an improved SA (ISA) with mathematical programming (MP) to generate a hybrid
approach (ISA-MP) for solving the dynamic double-row layout problem (DDRLP). In
the proposed hybrid algorithm, a mixed solution coding scheme is applied to represent
both the combinatorial and continuous aspects of DDRLP, and four operators are
devised to enhance the effectiveness of the algorithm. In addition, MP is applied to
solutions obtained by ISA so as to further improve the solution quality. Computational
experiment results showed that the ISA can find optimal solutions for small-size
problems and obtain satisfactory solutions for problems with realistic size. Tayal and
Singh (2016) solved a multi-objective SDFLP using a hybrid algorithm (Hybrid
FA/CSA) which integrates two metaheuristics, firefly algorithm (FA) and chaotic SA
(CSA). In the proposed Hybrid FA/CSA, exploration capability of FA is utilized to get
an initial solution and followed by CSA, which exploits the local search space to
improve the initial solution. This Hybrid FA/CSA was also used by Tayal et al. (2016)
for solving a sustainable SDFLP. Shafigh et al. (2017) proposed a hybrid heuristic
algorithm to solve a comprehensive model for distributed layout design with production
planning and systems reconfiguration. This hybrid heuristic algorithm is a linear
programming (LP) embedded SA with multiple search paths. In this hybrid approach,
SA searches over the discrete variables in the problem solution space and the
corresponding continuous variables are determined by solving a LP sub-problem using a
simplex algorithm. Since there may be infinite combinations of the values for the
continuous variables, by solving a LP sub-problem, values that optimally correspond to
the integer solution can be obtained easily. Besides, some constraints having continuous
variables in their equations may be difficult to satisfy by using stochastic search of the
SA alone, but they can be satisfied by solving the LP sub-problem. Computational
experiments showed that the proposed hybrid heuristic has very encouraging
performance.
Some researchers have built hybrid algorithms based on ACO. McKendall Jr
and Shang (2006) modified the hybrid ant system (HAS–QAP) developed by
Gambardella et al. (1999) and create three HASs (HAS I, HAS II, HAS III) for DFLP.
In HAS I, a random descent pairwise exchange technique is used to improve the initial
set of solutions and the set of modified solutions. HAS II uses a SA instead of the
random decent pairwise exchange heuristic for local search, which is the only difference
between HAS I and HAS II. HAS III is exactly like HAS I except that it adds a look-
ahead/look-back strategy to the random decent pairwise exchange heuristic. It showed
that all the proposed HASs perform well in computational experiments. Chen and
Rogers (2009) investigated a multi-objective DFLP which includes both quantitative
(distance-based) and qualitative (adjacency-based) objectives. They proposed an ACO
algorithm to solve this problem, which is also expanded from the HAS-QAP developed
by Gambardella et al. (1999) with a simple but effective data structure and solution
generation mechanism. Yu-Hsin Chen (2013) modified the HAS I and HAS III of
McKendall Jr and Shang (2006) and established two new heuristics named Binary
Coded HAS I (BC-HAS I) and Binary Coded HAS II (BC-HAS II). The difference
between BC-HAS I and BC-HAS II is that they do not adopt the same local search
strategy. BC-HAS I uses a pair-wise exchange heuristic for local search, whereas BC-
HAS II adopts the look-ahead/look-back strategy.
Several studies presented hybrid algorithms incorporating more than two
techniques. Kaveh et al. (2014) established a hybrid intelligent algorithm combining
GA, SA and fuzzy simulation together to solve the three fuzzy models proposed for
DFLP. Hosseini et al. (2014) presented a robust and simply structured hybrid algorithm
by integrating three metaheuristics, namely, ICA, SA, and VNS, which can solve the
DFLP efficiently. In this hybrid algorithms, ICA and VNS are applied for
diversification, while VNS and SA are used to ensure intensification capability.
Other hybrid approaches proposed in the literature are summarized as follows.
Erel et al. (2003) presented a new hybrid heuristic for DFLP, which has three stages. In
the first stage, a set of layouts that are likely to appear in the optimal solution are
selected. Since the DFLP can be regarded as a shortest path problem, in the second
stage, viable layouts obtained from the previous stage are used to solve this shortest
path problem by DP. In the last stage, a local improvement process is included to
improve the solutions obtained from the second stage. It was shown that the proposed
heuristic can solve large scale DFLP. Azimi and Charmchi (2012) developed a new
efficient heuristic algorithm integrating integer programming and discrete event
simulation to address DFLP with budget constraint. In this algorithm, the nonlinear
DFLP model has been changed to a pure integer programming model. They then used
the optimal solution of the linear model in a simulation model to determine the
probability of assigning facilities to certain locations. The simulation model obtains
near-optimal solution after sufficient number of runs. The test results showed that the
proposed heuristic is more efficient in terms of speed and accuracy than the heuristics
reported in the paper of Şahin et al. (2010). Rezazadeh et al. (2009) extended the
discrete particle swarm optimization (DPSO) developed by Liao et al. (2007) to solve
the DFLP. They used the semi-annealing approach, a SA with only the outer loop as the
local search technique in DPSO. The performance of the proposed DPSO was compared
with other solving methods developed in existing literature including DP, GA, SA,
HAS, hybrid simulated annealing (SA-EG), hybrid genetic algorithms (NLGA and
CONGA). The results showed that the proposed DPSO performs better than all the
other approaches and has a good computational efficiency for larger scale problems.
Hosseini-Nasab and Emami (2013) developed a hybrid PSO (HPSO) algorithm to solve
DFLP, in which a simple and fast SA is used for local search.
Table 6 Summary of DFLP studies by solution methodology.
Exact Methods Authors
B&B Lahmar and Benjaafar (2005), Kheirkhah and Bidgoli (2016)
DP Chen (1998), Urban (1998)
MSG Ulutas and Saraç (2012)
Heuristics Authors
Yang and Peters (1998), Balakrishnan et al. (2000), Lahmar and
Benjaafar (2005), Balakrishnan and Cheng (2009), Chan and
Malmborg (2010), Ripon et al. (2011a), Kumar and Prakash Singh
(2017)
Metaheuristics Authors
SA
Baykasoğlu and Gindy (2001), McKendall Jr et al. (2006), Ashtiani
et al. (2007), Dong et al. (2009), Şahin et al. (2010), Shahbazi
(2010), Pillai et al. (2011), Kia et al. (2012), Moslemipour and Lee
(2012), Emami and Nookabadi (2013), Kia et al. (2013), Kia et al.
(2015), Li et al. (2015), Kheirkhah and Bidgoli (2016), Tayal et al.
(2016), Pourvaziri and Pierreval (2017)
TS
Kaku and Mazzola (1997), McKendall and Jaramillo (2006),
Kulturel-Konak et al. (2007), McKendall Jr (2008), McKendall Jr
and Hakobyan (2010), Shahbazi (2010), McKendall Jr and Liu
(2012), Bozorgi et al. (2015)
GA
Kochhar and Heragu (1999), Balakrishnan and Cheng (2000),
Krishnan et al. (2008), Yang et al. (2011), Emami and Nookabadi
(2013), Mazinani et al. (2013), Kia et al. (2014), Vitayasak et al.
(2016)
ACO Corry and Kozan (2004), Baykasoglu et al. (2006), Ning et al.
(2010), Chen and Lo (2014)
PSO Jolai et al. (2012), Derakhshan Asl and Wong (2015), Kheirkhah et
al. (2015), Xu and Song (2015)
AIS Ulutas and Islier (2009), Ulutas and Islier (2010), Ulutas and Islier
(2015)
Fuzzy Ning et al. (2010), Samarghandi et al. (2013), Kaveh et al. (2014),
Xu and Song (2015), Xu et al. (2016)
Others
Urban (1998): GRASP, initialized multigreedy algorithm
Ming et al. (2002): SymEA
Abedzadeh et al. (2013): VNS
Kheirkhah and Bidgoli (2016): ICA
Hybrid Authors
Balakrishnan et al. (2003), Dunker et al. (2005), Erel et al. (2003),
Krishnan et al. (2006), McKendall Jr and Shang (2006), Chen and
Rogers (2009), Rezazadeh et al. (2009), Şahin and Türkbey (2009),
Ripon et al. (2011b), Azimi and Charmchi (2012), Hosseini-Nasab
and Emami (2013), Yu-Hsin Chen (2013), Hosseini et al. (2014),
Kaveh et al. (2014), Pourvaziri and Naderi (2014), Kulturel-Konak
and Konak (2015), Uddin (2015), Wang et al. (2015), Tayal et al.
(2016), Tayal and Singh (2016), Shafigh et al. (2017)
4 Conclusion and future directions
This paper reviews the DFLP studies published since the survey by Balakrishnan and
Cheng (1998) was conducted. At the beginning of this paper, different features of DFLP
are discussed in terms of problem formulations, objectives, constraints as well as
facility characteristics. Regarding problem formulations, modified QAP and MIP appear
to be the most popular forms. Besides, the DFLP is also modelled using GT, game
theoretic model and DEA. To address the uncertainties in production, several studies
apply stochastic modelling for DFLP, thereby transforming DFLP to SDFLP. In
addition, a stream of studies model uncertainties using fuzzy logic. In the past two
decades, a number of studies consider multiple objectives in DFLP, including both the
conventional quantitative objective (cost minimization) and qualitative objectives such
as maximizing adjacency rate, minimizing shape ratio etc., so as to make the problem
more realistic. Special constraints are also considered in DFLP modelling, which mainly
include position constraints (e.g. non-overlapping, orientation and pick-up/drop-off
points), budget constraints and capacity constraints. DFLP studies are also characterized
by different manufacturing systems, layout configurations, and facility shapes. For
example, a number of researchers focus on cellular layout, while some specifically deal
with single-row layout, and some define facility shape using aspect ratio instead of
fixed dimensions.
Different solution methods implemented for solving DFLPs are also discussed in
details. In recent years, a few researchers used exact approaches to find optimal
solutions for DFLP. These methods generally work well on small-sized DFLPs. As
recent DFLP studies are trying to capture more specific features in different
manufacturing environments, the DFLP models have become more realistic yet more
complex in computation. Hence, metaheuristics have become the most widely used
approaches (56 out of 77), especially in the last decade (see Figure 2). Among the
different metaheuristics adopted, SA is the most popular method followed by TS and
GA (see Figure 3).
Further, in the past decade, novel metaheuristics such as PSO, AIS and fuzzy
system have been introduced in DFLP research for solving problems with multiple
objectives, uncertainties and special constraints. Also, there is increasing interest in
hybrid algorithms as they can overcome the weakness of using a pure method by
incorporating other approaches so as to enhance computational capability and to
improve the solution quality. In hybrid algorithms, the use of GA is frequent, with pair-
wise exchange heuristics and SA being commonly used in local search.
Future research in DFLP could include custom objective functions and
constraints to depict realistic problems more accurately, such as considering multiple
cooperative or conflicting objectives, dynamic transportation costs during a single
period (Samarghandi et al. 2013), time-dependent rearrangement cost, departments with
variable shapes, new constraints related to facilities or different characteristics for the
unsuitability between departments and locations (Azevedo et al. 2017). So far, a number
of researchers have already attempted to solve DFLP with multiple floors, unequal area
departments, uncertainties in the demand forecast, budget constraint, pick-up/drop-off
points, however further exploration of DFLPs with these characteristics are still needed.
Incorporating with BDA and DEA in DFLP has been investigated by a few researchers
to deal with more complex and realistic problems and determine the most efficient
layout. Hence, investigating other analytic methods in the DFLP is also a possible future
direction. Besides, the DFLP can also be integrated with more detailed layout
configuration for each department at operational level to create powerful decision
support systems (Azevedo et al. 2017). Real life circumstance and data (including
factory data and big data) may also be considered in the DFLP for future work (Li et al.
2015, Tayal and Singh 2016). In addition, Ulutas and Islier (2010) used the concept of
DFLP to solve the dynamic content area layout for internet newspapers, which indicates
the possibility of applying DFLP to other relevant problems in the digital age.
As DFLP studies are focusing on more and more complicated and realistic
scenarios, efficient solving methods are required. Metaheuristics and hybrid schemes
are the most promising approaches for solving complex and large-sized DFLPs. In
regard to metaheuristics, researchers can improve current metaheuristics or develop
novel metaheuristics techniques to create more effective solutions. For hybrid schemes,
combining different algorithms can overcome the drawbacks of a single algorithm type
method so as to make it possible for generating good solutions for larger and more
practical problems with realistic constraints and objectives. For example, the features of
TS such as tabu list, adaptive memory, diversification and intensification may be added
to the SA algorithms to obtain better computational results (Şahin and Türkbey 2009).
Different local search procedures can also be applied in sophisticated hybrid schemes to
develop effective approaches and achieve better solutions in complex DFLPs. Also, the
proposed algorithms for DFLPs can be tried on the other well-known combinatorial
optimisation problems such as the vehicle routing problem and travelling salesman
problem. (Pourvaziri and Naderi 2014, Şahin and Türkbey 2009). Given the nature of
today’s business environment where demand may be difficult to predict, the more use of
fuzzy methods (Azimi and Charmchi 2012), and game theory (Kheirkhah and Bidgoli
2016) in research would be attractive avenues in increasing realism in DFLP models.
Finally, the application of more sophisticated statistical analysis of the results
(Baykasoglu et al. 2006) and the application of design of experiments such as Taguchi
methods is also desirable (Ulutas and Islier 2009).
Figure 2 DFLP research classified by solution methodology.
Figure 3 DFLP studies classified by metaheuristics algorithms.
5 Acknowledgement
This research is partially supported by grants from General Research Fund of Research
0
5
10
15
20
25
30
35
40
45
50
Exact Heuristic Metaheuristics Hybrid
Nu
mb
er o
f st
ud
ies
Solution Methodology
1998-2007
2007-Now
SA 17.31%
TS 8.15%
GA 9.16%
ACO 4.7%
PSO 5.9%
AIS 2.4%
Fuzzy 6.11%
Other 4.7%
Grant Council of Hong Kong (Project No. 14615015) as well as from the Canadian
Centre for Advanced Supply Chain Management and Logistics at the Haskayne School
of Business.
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